Phase-stability analysis of the magnetron-driven vircator experiment

A slow envelope approximate solution to the Van der Pol equation is evaluated as a model for a driven high-power oscillator experiment. It is shown that Adler´s inequality gives a necessary but not sufficient condition for achieving phase-locking between the driving relativistic magnetron and the driven high-power cavity vircator oscillations. The amplitude of the entrained (phase-locked) oscillations is found as a function of the injected magnetron power, the initial frequency detuning, and other system parameters. The stability of these oscillations is examined. Not all entrained states are stable. Parameteric boundaries between stable and unstable states are given. Combination oscillations containing both magnetron and vircator frequency components are predicted and observed to occur when the initial detuning between the two sources is too large to allow entrainment